I was in a production of it in 1999.
Apart from "Kids", other well-known songs from the show include "Put on a Happy Face", and "Gotta lot of living to do". Lesser known are "Last Kiss" and "Spanish Rose".
And yes, "We love you Beatles" was a copy of "We love you Conrad": the reprise bit is the fact that the adoring fans keep coming back and singing "We love you Conrad" at various intervals in the show.
It probably was more a comment on Elvis Presley's life history, as Conrad similarly gets drafted into the Army.